Eliot Richards' late equaliser got new Bristol Rovers manager John Ward's second spell at the club off to an unbeaten start.
Michael Hector put the Shots ahead from the edge of the area, before David Clarkson equalised from the spot after Aaron Morris fouled Tom Eaves.
Craig Reid's penalty looked to have won the game for the hosts, following a foul by Tom Parkes on Sonny Bradley.
But Richards rescued a point for the Pirates with a scuffed shot late on.
Despite Richards' goal, Rovers remain bottom of League Two, while Aldershot are 22nd, just three points above the drop-zone.
VIEW FROM THE DRESSING ROOM
Aldershot Town manager Dean Holdsworth told BBC Surrey:
"I'm disappointed with the result, but I thought the team played excellently.
"There are positives to take and we have another home game soon, so we've got to build on that.
"We thought we'd play some excellent football, but this just didn't make for a good match.
"We know that we want positive play and the players need to pick themselves up and take it in to Saturday."
Aldershot 21 Young 03 Tonkin 04 Morris 05 Brown 11 Vincenti (Berqvrst - 85' ) 23 Bradley 39 Hector 28 Cadogan (Mekki - 73' ) 31 Rose 10 Hylton (Reid - 72' ) 37 Lopez Substitutes 29 Morris 16 Berqvrst 17 Mekki 33 Roberts 40 Webbe 20 Reid 27 Madjo Bristol Rovers 28 Walker 02 Smith 05 Kenneth 06 Parks 11 Broghammer 29 Bolger 03 Paterson (Brown - 18' ) 25 Clucas (Richard - 80' ) 07 Clarkson (Norburn - 73' ) 16 Anyinsah 32 Eaves Substitutes 20 Gough 14 Brown 15 Norburn 10 Richard 17 Harrison 18 Harding 33 Santos